Question

As part of his semester project, a BYU-Idaho Introductory Statistics student calculates a 95% confidence interval for the true percentage of BYU-Idaho students who are from Latin America. What does the phrase "95% confidence" mean?
a. There's a 95% chance that the true proportion is in the confidence interval.
b. 95% of the student's data are within the confidence intervals.
c. If we create many 95% confidence intervals, 95% of them will contain the true proportion.
d. The sample proportion is in 95% of the confidence intervals we make.

Answer 1

Answer:

a. There's a 95% chance that the true proportion is in the confidence interval.

Step-by-step explanation:

When we want to estimate a property of a population (a population's parameter), without surveying the population, we use samples.

Then, with the information of the samples we can calculate the statistics and infere properties about a population. This inferences obviously came with some uncertainty, depending on the properties of the sample and specially the sample size.

When we talk about confidence intervals, we use the statistic of the sample (in this case, the mean) to estimate a range of values it is expected to find the true mean of the population. The width of this interval depends on the sample standard deviation and the sample size.

The value of the confidence interval (95%, 99%, etc) represent the probabilty that the true mean is within this interval.